In most countries (I'm open to counter-examples) a president is expected to be above the fray of party politics. If picking a sitting minister is a serious possibility, then it's clearly not a consideration in Germany.

And I have no idea why the SPD or Grünen would contribute to electing a CDU partisan.

It is rightly acknowledged that people of faith have no monopoly of virtue
- Queen Elizabeth II

In most countries (I'm open to counter-examples) a president is expected to be above the fray of party politics. If picking a sitting minister is a serious possibility, then it's clearly not a consideration in Germany

We would expect them to switch to presidential mode the moment they are elected. If they don't manage that, we could try to force them to resign. By the way, all our presidents with only one exception were catastrophes.

And I have no idea why the SPD or Grünen would contribute to electing a CDU partisan

Because they can't dream of a majority without Die Linke. And a coalition with Die Linke is impossible because all members of that party are dirty and stink, and are stalinists, and eat babies for breakfast. So, Greens OR SPD can form a coalition with the CDU but not with each other.

Weizsäcker is a typical representative of his generation that never knew anything, for instance what his regiment did in Russia. He didn't know. Later he didn't know that the US made Agent Orange from the chemicals he sold them.

Like his father, Nazi, Reich Foreign Secretary before becoming ambassador to the Vatican, who said at his trial he didn't know Jews were being killed at Auschwitz. Richard von W, then a law student, was assistant counsel to his father at that trial.

He was a law student and defending his own father. Nothing wrong with that. He associated with his father in regard to the father's guilt. Well, it was his father. This did not make the son guilty (though probably naïve). I blame Richard v.W. for his intentional amnesia concerning his own role in the holocaust and the cruelties against Russians.

"In most countries (I'm open to counter-examples) a president is expected to be above the fray of party politics. "

In most countries a president is picked put of a number of party politicians with a long political career. It is true that the politician is then supposed to be able to rise about party politics.

"If picking a sitting minister is a serious possibility, then it's clearly not a consideration in Germany."

Mostly partisan alingment and fitness to act as above parties are both taken into consideration. Scheel did go directly from minister to president, Weizsäcker from state prime minister to president. Others like Rau had some time without office, but that is not considered as necessary.

"And I have no idea why the SPD or Grünen would contribute to electing a CDU partisan."

Because they have no majority of their own in the assembly electing the president.